论文标题
带有热扩散效果的Bresse-Timoshenko型系统：稳定，稳定性和数值结果
Bresse-Timoshenko type systems with thermodiffusion effects: Well-possedness, stability and numerical results
论文作者
论文摘要
研究了具有热，质量扩散和神经弹性效应的Bresse-Timoshenko束模型。我们陈述并证明了问题的良好性。通过使用经典的Faedo-Galerkin近似值以及两个先验估计值来证明解决方案的全局存在和唯一性。我们证明了在异常假设下的问题的指数稳定性估计，并且通过在两种不同的情况下使用乘数技术，在角度旋转中摩擦阻尼，并在垂直位移中进行摩擦阻尼。在数值零件中，我们首先通过$ p_1 $ -finite元素方法获得了用于空间离散化的数值方案，并获得了时间离散化的隐式Euler方案。然后，我们证明了离散的能量衰减，后来建立了先验误差估计。最后，提出了一些数值模拟。
Bresse-Timoshenko beam model with thermal, mass diffusion and theormoelastic effects is studied. We state and prove the well-posedness of problem. The global existence and uniqueness of the solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate for problem under an unusual assumption, and by using a multiplier technique in two different cases, with frictional damping in the angular rotation and with frictional damping in the vertical displacement. In numerical parts, we first obtained a numerical scheme for problem by $P_1$-finite element method for space discretization and implicit Euler scheme for time discretization. Then, we showed that the discrete energy decays, later a priori error estimates are established. Finally , some numerical simulations are presented.
